If you want to know how we calculate the amount of fencing materials you need, here is a list of the equations we used:
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Number ofposts⏟round the result up=Fence lengthPost spacing+1\scriptsize \underbrace{\begin{gather*}\rm Number\ of\\[-5px]\rm posts \end{gather*}}_{\text{round the result up}} = \mathrm{\frac{Fence\ length}{Post\ spacing} + 1}
round the result up
Number
of
posts
=
Post
spacing
Fence
length
+
1
Number ofsections=Numberof posts−1\scriptsize \begin{gather*}\rm Number\ of\\[-5px]\rm sections \end{gather*} = \begin{gather*}\rm Number\\[-5px]\rm of\ posts \end{gather*} - 1
Number
of
sections
=
Number
of
posts
−
1
Post length=1.5×Fence height\scriptsize \mathrm{Post\ length = 1.5 \times Fence\ height}
Post
length
=
1.5
×
Fence
height
Number ofrails=Railsper section×Numberof sections\scriptsize \begin{gather*}\rm Number\ of\\[-5px]\rm rails \end{gather*} = \begin{gather*}\rm Rails\\[-5px]\rm per\ section \end{gather*} \times \begin{gather*}\rm Number\\[-5px]\rm of\ sections \end{gather*}
Number
of
rails
=
Rails
per
section
×
Number
of
sections
Number ofpickets⏟round the result up=Fence lengthPicketwidth+Picketspacing\scriptsize \underbrace{\begin{gather*}\rm Number\ of\\[-5px]\rm pickets \end{gather*}}_{\text{round the result up}} = \frac{\text{Fence length}}{\begin{gather*}\rm Picket\\[-5px]\rm width \end{gather*}+ \begin{gather*}\rm Picket\\[-5px]\rm spacing \end{gather*}}
round the result up
Number
of
pickets
=
Picket
width
+
Picket
spacing
Fence length
The volume of the hole minus the volume of the part of the post that's underground (buried post volume) results in the concrete volume for one post:
Concretevolume⏟for one post=Holevolume−Buriedpostvolume\scriptsize \underbrace{\begin{gather*}\rm Concrete\\[-5px]\rm volume \end{gather*}}_{\text{for one post}} = \begin{gather*}\rm Hole\\[-5px]\rm volume \end{gather*} - \begin{gather*}\rm Buried\\[-5px]\rm post\\[-5px]\rm volume \end{gather*}
for one post
Concrete
volume
=
Hole
volume
−
Buried
post
volume
Once you know the concrete volume for one post, multiply it by the number of posts, and you'll get the total concrete volume for the entire fence.
To calculate the hole volume and the buried volume, we'll need the post depth, which must be at least ⅓ of the post length:
Postdepth=Post length3\scriptsize \begin{gather*}\rm Post\\[-5px]\rm depth \end{gather*} = \frac{\text{Post length}}{3}
Post
depth
=
3
Post length
Now, let's look at how to calculate the volumes for the two types of posts.
For the cuboid post, the recommendation is to use a rectangular hole with three times the width and thickness of the post:
Holevolume=3×Postwidth×3×Postthickness×Postdepth\scriptsize \begin{gather*}\rm Hole\\[-5px]\rm volume \end{gather*} \!\!=\!\! 3 \!\times\! \begin{gather*}\rm Post\\[-5px]\rm width \end{gather*} \!\times\! 3 \!\times\! \begin{gather*}\rm Post\\[-5px]\rm thickness \end{gather*} \!\times\! \begin{gather*}\rm Post\\[-5px]\rm depth \end{gather*}
Hole
volume
=
3
×
Post
width
×
3
×
Post
thickness
×
Post
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depth
Buriedpostvolume=Postwidth×Postthickness×Postdepth\scriptsize \begin{gather*}\rm Buried\\[-5px]\rm post\\[-5px]\rm volume \end{gather*} = \begin{gather*}\rm Post\\[-5px]\rm width \end{gather*} \times \begin{gather*}\rm Post\\[-5px]\rm thickness \end{gather*} \times \begin{gather*}\rm Post\\[-5px]\rm depth \end{gather*}
Buried
post
volume
=
Post
width
×
Post
thickness
×
Post
depth
From the formulas above, we can obtain a final and easier-to-calculate equation for the concrete volume:
Concretevolume⏟for one post=8×Postwidth×Postthickness×Postdepth\scriptsize \underbrace{\begin{gather*}\rm Concrete\\[-5px]\rm volume \end{gather*}}_{\text{for one post}} \!=\! 8 \!\times\! \begin{gather*}\rm Post\\[-5px]\rm width \end{gather*} \!\times\! \begin{gather*}\rm Post\\[-5px]\rm thickness \end{gather*} \!\times\! \begin{gather*}\rm Post\\[-5px]\rm depth \end{gather*}
for one post
Concrete
volume
=
8
×
Post
width
×
Post
thickness
×
Post
depth
Remember that you must multiply the concrete volume above by the number of posts to obtain the total concrete volume.
For the cylindrical post, we do something similar: use a hole whose diameter is three times the post diameter:
Holevolume=π4×(3×Postdiameter)2×Postdepth\scriptsize \begin{gather*}\rm Hole\\[-5px]\rm volume \end{gather*} \!=\! \frac{\pi}{4} \times \left(3 \times \begin{gather*}\rm Post\\[-5px]\rm diameter \end{gather*} \right)^2 \times \begin{gather*}\rm Post\\[-5px]\rm depth \end{gather*}
Hole
volume
=
4
π
×
(
3
×
Post
diameter
)
2
×
Post
depth
Buriedpostvolume=π4×(Postdiameter)2×Postdepth\scriptsize \begin{gather*}\rm Buried\\[-5px]\rm post\\[-5px]\rm volume \end{gather*} = \frac{\pi}{4} \times \left(\begin{gather*}\rm Post\\[-5px]\rm diameter \end{gather*} \right)^2 \times \begin{gather*}\rm Post\\[-5px]\rm depth \end{gather*}
Buried
post
volume
=
4
π
×
(
Post
diameter
)
2
×
Post
depth
From the two formulas above, we can also obtain an easier equation for the concrete volume:
Concretevolume⏟for one post=2×π×(Postdiameter)2×Postdepth\scriptsize \underbrace{\begin{gather*}\rm Concrete\\[-5px]\rm volume \end{gather*}}_{\text{for one post}} \!=\! 2 \!\times\! \pi \!\times\! \left(\begin{gather*}\rm Post\\[-5px]\rm diameter \end{gather*} \right)^2 \!\times\! \begin{gather*}\rm Post\\[-5px]\rm depth \end{gather*}
for one post
Concrete
volume
=
2
×
π
×
(
Post
diameter
)
2
×
Post
depth
Again, multiply the concrete volume above by the number of posts to obtain the total concrete volume.
💡 Remember that π≈3.1416\pi \approx 3.1416π≈3.1416
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